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One presents a simple Set Theory Model (STM) of the valid categoricalarguments (VCAs) - a proper superset of the valid (categorical) syllogisms(VS). The main STM initiator was George Boole, who worked with a universe ofdiscourse, U, which contains the pairwise complementary sets, or categoricalterms, S, non-S, P, non-P, M, non-M, and is thus partitioned into eightsubsets: SPM, SP(non-M),...,(non-S)(non-P)(non-M), where the intersection wasdenoted by adjacency. In STM all superfluous syllogistic figures aredisregarded, and both the positive terms, S, P, M, and the negative terms,non-S, non-P, non-M, are allowed to appear in the pairs of categorical premises(PCPs) and their entailed logical consequences (LCs). This increases the numberof distinct P (resp. S) premises from the six formulable via only positiveterms, to eight, and the number of distinct PCPs from the 36 appearing in theClassical Categorical Syllogistic (CCS), to the 64 appearing in the STM. Out ofthe latter 64 PCPs, only 32 PCPs entail LCs and thus generate VCAs. These VCAs,(and the VS), split into four types. Each type contains eight VCAs. Any VCA canbe re-written as any other VCA of the same type, via a group G of eightre-labelings. Thus the VCAs Barbara, Darapti, Darii, Disamis, can be chosen astype representatives for both VCAs and VS, and via a term relabeling, any VCAor VS can be re-written, without changing their PCP or LC contents, as either aBarbara, Darapti, Darii, or Disamis. One discusses the VCAs and their LCs,simple/biliteral VCA sorites, empty set constraints (ESC), VCA distributionconservation, and other Rules of Valid Categorical Arguments (RofVCA) which areVCA generalized versions of some of the Rules of Valid Syllogisms (RofVS). Notethat CCS restricts the VS to only LCs of the formats A(S,P), E(S,P), I(S,P),O(S,P).

An extension of valid syllogisms to valid categorical arguments, and a  reduction of the latter to only Barbara, Darapti, Darii and Disamis. To the  memory of my sister Cristina Popa, 1948-2018